By [1]}, there exists a unique system of functions \(\tau _V(A,B,C)\)  which satisfies the above Properties (REF ) through (REF ), so the definition makes sense. One can think of the Maslov ternary index as a kind of “cross ratio” of triplets of Lagrangians in a symplectic vector space. If \((A,B)\)  and \((A^{\prime },B^{\prime })\)  are two pairs of transverse Lagrangians in a symplectic vector space one can find a symplectic automorphism \(\varphi \)  such that \(\varphi (A)=A^{^{\prime }}\)  and \(\varphi (B)=B^{^{\prime }}\) . However, the symplectic group does not act transitively on triples of Lagrangians. In fact The configuration of three transverse Lagrangians is completely determined by their index.
